🔭 Watchtower Horizon: Curvature, Refraction and the Hidden Part of a Boat (2D)

Side view of a lookout on a river watch tower over the curved Earth: the sight line to the horizon, the ground that drops away, and a boat or beacon far off whose lower part is hidden. Set the platform height, the mast height, the distance and the air refraction, and see the horizon distance, the dip, the greatest distance at which the mast top can be seen and how much of the boat is below the horizon. The exact tangent, a ray-tracing search, a bisection for the hidden height and the refraction gain are checked numerically, with four in-page numerical checks.